Basic notions reading group — Fall 2013


Organization

Organization
All participants, but questions may be directed to Johan Commelin
Location
Hilbertruimte
Time
Mondays, 14.00–15.00

Description

We will treat some topics (mostly categorical) that are useful for algebraic topologists and algebraic geometers. The focus will lie on Grothendieck topoi, and related notions. Besides that we will deal with some more algebraic concepts, aimed at cohomology.

A provisional list of topics:


Schedule

7 Oct 2013
Introduction. Quick review of: sheaves on Open(X); equivalence with étalé bundles. Definition of coverages and Grothendieck topology. Sheaves on a site (definition relative to covarages, relative to sieves, and their equivalence).
14 Oct 2013
Johan Commelin — Sheafification on a site (definition, properties: adjunction, idempotence, exactness). [Notes]
21 Oct 2013
Frank Roumen — Grothendieck topoi: examples and basic properties. [Notes]
28 Oct 2013
Joost Nuiten — Commutative group objects in an elementary topos form an abelian category.
4 Nov 2013
No meeting.
11 Nov 2013
Joost Nuiten — Commutative group objects in a Grothendieck topos have enough injectives.
18 Nov 2013
Giovanni Caviglia — Geometric morphisms. [Notes]
25 Nov 2013
Frank Roumen — Points of a topos.

Literature

We will be using several sources as reference material.


Participants

If you would like to participate in this seminar, please send me an email. (My email address is on my homepage.)